Abstract Rockfall frequency size distributions are used in Austria for the definition of a design block for the planning of technical rockfall protection. Rockfall size datasets are often incomplete. Here, we study fifteen catalogues of rockfall size in Austria, Italy, and the USA to analyse the impact of the data collection and mapping methods on the representativeness of the catalogues and on the estimates of frequency-size statistics. To describe and compare the catalogues of rockfall size, we first use Empirical Cumulative Distribution Functions (ECDFs), followed by parametric distribution estimates in the form of Probability Density Functions (PDFs), and Cumulative Distribution Functions (CDFs). We discuss the output of Kolmogorov-Smirnov tests, the position of the frequency-size distribution rollover, and the p-value and the standard errors associated to the distribution parameters estimates to determine the reliability of our model results. In addition, we analyse the variations in the modelled CDFs for different percentiles of the frequency-size distributions to describe and discuss the representativeness of the rockfall catalogues. Our results show that different mapping strategies may affect the estimates of frequency-size distribution of rock fall volume, a relevant information when evaluating the possible impacts of rockfall processes. We conclude offering recommendations for rockfall mapping, and the use and of a non-parametric statistical method being capable to deal with small datasets, which is very typical when dealing with rockfall data. Such recommendations help for a correct dimensioning of designing rockfall mitigation measures.

中文翻译：

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测绘策略对落石频率-大小分布的影响

摘要 落石频率大小分布在奥地利用于定义落石技术保护规划的设计块。落石大小数据集通常不完整。在这里，我们研究了奥地利、意大利和美国的 15 个落石大小目录，以分析数据收集和制图方法对目录代表性和频率大小统计估计的影响。为了描述和比较落石大小的目录，我们首先使用经验累积分布函数 (ECDF)，然后是概率密度函数 (PDF) 和累积分布函数 (CDF) 形式的参数分布估计。我们讨论 Kolmogorov-Smirnov 检验的输出，频率大小分布翻转的位置，以及与分布参数估计相关的 p 值和标准误差，以确定我们模型结果的可靠性。此外，我们分析了频率大小分布的不同百分位数的建模 CDF 的变化，以描述和讨论落石目录的代表性。我们的结果表明，不同的制图策略可能会影响落石量频率大小分布的估计，这是评估落石过程可能影响的相关信息。我们总结了对落石映射的建议，以及能够处理小数据集的非参数统计方法的使用和处理，这在处理落石数据时非常典型。此类建议有助于正确确定落石缓解措施的设计尺寸。